Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Caicedo-Casso A, Kang HW, Lim S, Hong CI - Sci Rep (2015)

Bottom Line:
Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology.In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type.We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

ABSTRACTBiological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

f6: Distribution of averaged half-life of autocorrelations.Model 2 and Model 5 adopt positive regulation via autocatalytic process, while Model 2′ and Model 5′ adopt positive regulation via inhibitory degradation. With each model, we considered 100 random parameter sets with stochastic noise and obtained the distribution of averaged half-life of autocorrelations. Red line in each panel exhibits the averaged half-life of autocorrelation with the default parameter set. For each case, a total of 1000 realizations of the Gillespie algorithm with volume factor N = 10 were performed. All parameter values were varied except critical thresholds and Hill coefficients. The values μ and σ in each panel stand for the mean and standard deviation of averaged half-life of autocorrelations, respectively.

Mentions:
As mentioned before, we considered two types of positive feedback, i.e., autocatalytic process and inhibitory degradation. We wondered which positive feedback does enhance the robustness of period in the presence of both internal and external noises. To test this, we modified Model 2 and Model 5 by switching autocatalysis to inhibitory degradation, called Model 2′ and Model 5′, respectively (see Supplementary Table S1). We found that positive feedback via autocatalysis makes the system more robust in period regardless of noise type, see Fig. 6. In this figure, we considered 100 random parameter sets together with stochastic noise and obtained the distribution of averaged half-life of autocorrelations. It is clear that the distribution is more concentrated at the higher averaged half-life when the autocatalytic positive regulation is employed in the system. Therefore, we can conclude that the autocatalytic positive feedback enhances the robustness of period in the presence of both external and internal noises when compared with inhibitory degradation model.

f6: Distribution of averaged half-life of autocorrelations.Model 2 and Model 5 adopt positive regulation via autocatalytic process, while Model 2′ and Model 5′ adopt positive regulation via inhibitory degradation. With each model, we considered 100 random parameter sets with stochastic noise and obtained the distribution of averaged half-life of autocorrelations. Red line in each panel exhibits the averaged half-life of autocorrelation with the default parameter set. For each case, a total of 1000 realizations of the Gillespie algorithm with volume factor N = 10 were performed. All parameter values were varied except critical thresholds and Hill coefficients. The values μ and σ in each panel stand for the mean and standard deviation of averaged half-life of autocorrelations, respectively.

Mentions:
As mentioned before, we considered two types of positive feedback, i.e., autocatalytic process and inhibitory degradation. We wondered which positive feedback does enhance the robustness of period in the presence of both internal and external noises. To test this, we modified Model 2 and Model 5 by switching autocatalysis to inhibitory degradation, called Model 2′ and Model 5′, respectively (see Supplementary Table S1). We found that positive feedback via autocatalysis makes the system more robust in period regardless of noise type, see Fig. 6. In this figure, we considered 100 random parameter sets together with stochastic noise and obtained the distribution of averaged half-life of autocorrelations. It is clear that the distribution is more concentrated at the higher averaged half-life when the autocatalytic positive regulation is employed in the system. Therefore, we can conclude that the autocatalytic positive feedback enhances the robustness of period in the presence of both external and internal noises when compared with inhibitory degradation model.

Bottom Line:
Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology.In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type.We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

ABSTRACTBiological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.